Related papers: Hilbert space formalisms for group field theory
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
We develop an approach to quantum dynamics based on quantum phase space trajectories. The latter are built from a unitary irreducible representation of the symmetry group of the respective classical phase space. We use a quantum action…
We will highlight that despite there being various approaches to quantum gravity, there are universal approach-independent features of quantum gravity. The geometry of spacetime becomes an emergent structure, which emerges from some purely…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion…
Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous…
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum…
We present a new point of view on the quantization of the gravitational field, namely we use exclusively the quantum framework of the second quantization. More explicitly, we take as one-particle Hilbert space, $H_{graviton}$ the unitary…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
We introduce the framework of Hopf algebra field theory (HAFT) which generalizes the notion of group field theory to the quantum group (Hopf algebra) case. We focus in particular on the 3d case and show how the HAFT we considered is…
For more than 80 years theoretical physicists have been trying to develop a theory of quantum gravity which would successfully combine the tenets of Einstein's theory of general relativity (GR) together with those of quantum field theory.…
Starting from a new understanding of the vacuum energy problem based on the combination of the phase space regularization and the holographic bound, we argue that quantum gravity should be understood as gravitized quantum theory, that is,…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…